Page 176 - Fundamentals of Radar Signal Processing

AC term only of the clutter to decorrelate to 10 percent of its power

(maximum correlation value) for wind speeds of 5, 15, and 25 mph.
Assume F = 1 GHz. Repeat for 10 GHz.
0
22. At the standard temperature of T = 290 K, at what frequency in hertz does
0
S (F) of Eq. (2.76) fall to 3 dB below its value at F = 0 Hz? It may be
n
necessary to find the answer numerically, but a small number of terms in
the series approximation to the exponential can be used to develop a good
initial estimate.

23. What is the effective noise temperature in kelvins for a system with a noise
figure of 3 dB? Repeat for 6 dB and 10 dB.

24. Consider an aircraft that has a radial velocity of Mach 2 (about 660 m/s)
away from a stationary L-band (1 GHz) radar. What is the difference in the

magnitude of the Doppler shift calculated from Eq. (2.93) and the
approximation resulting from Eq. (2.97)? Note: On some calculators, the
difference may be too small for the calculator precision. If this is the case,
try using MATLAB or a similar computational system to calculate the
®
difference; use format long in MATLAB to display more decimal
®
places than the default. The difference can also be estimated by
considering the largest term dropped from the series expansion [Eq.
(2.95)].

25. Suppose two aircraft are flying straight and level at the same altitude. At a
particular instant one is traveling due north at 100 m/s, while the other is
flying directly at the first but in the southwesterly direction. What is the
radial velocity between the two aircraft at that instant? What is the Doppler
shift in hertz, including the sign, at that instant?

26. A stationary radar with a rotating antenna (typical of an airport approach
radar, for instance) observes an aircraft moving through its airspace in a

straight line at a speed of 200 mph. The aircraft approaches from the east,
flies directly in front of the radar, and continues to the west. Sketch the
general behavior of the radial velocity of the target relative to the radar as
it flies from east to west through the airspace. Label significant values.

27. Derive an expression for the maximum radial velocity of a constant-radial
velocity target such that the total range migration in a CPI of M pulses
collected with a PRI of T seconds is less than the range resolution cτ/2.
The answer will be in terms of M, T, and τ. What is this velocity for a

relatively long (for Doppler processing purposes) CPI of 30 pulses at T =
1 ms and a pulse length of 10 μs?

28. In Eqs. (2.100) to (2.104) the time-varying range between a moving radar
and a stationary target was computed. A series expansion was used to
approximate the range as a quadratic function (specifically, a parabola),